Question

A company produces batteries. On average, 85% of all batteries produced are good. Each
battery is tested before being dispatched, and the inspector correctly classifies the battery 90%
of the time.
A. What percentage of the batteries will be “classified as good”?
B. What is the probability that a battery is defective given that it was classified as good?

Answer 1

Answer:

good afternoon this is a good question

Answer 2

Answer:

Me · Beginner

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Given : A company produces batteries. On average, 85% of all batteries produced are good. Each battery is tested before being dispatched, and the inspector correctly classifies the battery 90% of the time.

To find : A. What percentage of the batteries will be “classified as good”?

B. What is the probability that a battery is defective given that it was classified as good?

Solution:

Good Batteries = 85 %

Not good Batteries = 100 - 85 % = 15 %

inspector correctly classifies the battery 90% of the time.

=> 100 - 90 % = 10 % is incorrect classification

Classified Good batteries out of 85 % good = (90/100) 85 % = 76.5 %

Classified not good Batteries out of 85 % good = (10/100) 85 % = 8.5 %

Classified not Good batteries out of 15 % not good = (90/100) 15 % = 13.5 %

Classified Good Batteries out of 15 % not good = (10/100) 15 % = 1.5 %

percentage of the batteries classified as good = 76.5 + 1.5 = 78 %

Classified good and actual good = 76.5 %

Classified Good and actual not good ( defective) = 1.5 %

probability that a battery is defective given that it was classified as good

= (1.5)/(1.5 + 76.5)

= 1.5/78

= 1/52

= 1.92 %

78 % of the batteries will be “classified as good"

probability that a battery is defective given that it was classified as good = 1.92 %

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